
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
*“You have been beaten by a Gru”***p1.** All minions either have  $1$  or  $2$  eyes, and have one of  $4$  possible hairstyles. They are all thin and short, fat and short, or thin and tall. Gru doesn’t want to have any  $2$  minions that look exactly alike, so what is the maximum possible amoount of minions can he get?**p2.** Dave is shaped like two hemispeheres placed on either side of a vertical cylinder. If Dave is  $4$  feet across in width (excluding arms) , and has total volume  $20\pi$  feet $^3$  , then how tall is he? (excluding legs and hair)**p3.** There are  $400$  minions.  $120$  like Agnes,  $160$  like Margo, and  $180$  like Edith.  $37$  of the minions like both Agnes and Margo, and  $74$  minions like only Margo and Edith. If the number of minions that like all three girls to the number of minions that like Agnes and Edith to the number of minions that like none of the girls is  $1:2:3$ , how many minions like all  $3$  girls?**p4.** There is a circular chair, that has the same radius as a minion, so to seat him perfectly on the chair. Gru wants to save space, so he starts shooting them with the shrinking ray from the first movie. If the minions are  $1/5$  the size that they used to be (in diameter), how many minions can fit per chair?**p5.** Minion  $A$  fires a laser from a corner of a room to the opposite corner. The room has length  $32$  and width  $24$ . Minion  $B$  walks from the middle of the width side on one end of the room to as far as he can to the other side of the room along the length of the room. He stops right before he gets hit by the laser. What is the area of the total amount of area that the minion can walk over if he only walks left and right along the length of the room? The minion’s head from above angle has radius  $5$ .

PS. You should use hide for answers.

Present the answer in LaTex format: \boxed{Your answer}
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