
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

Thirty-three warriors were hired to guard Lukomorye for 240 coins. The cunning Uncle Chernomor can divide the warriors into groups of any size (or record all of them in one group) and then distribute all the wages among the groups. Each group divides its coins equally, and the remainder is given to Chernomor. What is the maximum number of coins that Chernomor can receive if:

a) Chernomor distributes the wages among the groups as he wishes;

b) Chernomor distributes the wages among the groups equally?

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