
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
A game stall on the street has a sign that says "Roll the dice, win the grand prize." The rules of the game are as follows: You can choose one number from 1, 2, 3, 4, 5, 6, place a bet of $m$ yuan, and then roll a die three times. If the number you bet on appears once, twice, or three times during the three rolls, the dealer will return your original bet and also give you a reward of 1, 2, or 3 times your bet, respectively. If the number does not appear at all during the three rolls, the dealer keeps your bet.
(1) Calculate the probability of getting at least one 5 in three dice rolls.
(2) If you plan to try the game once, calculate the expected value of your profit and provide proper advice.

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