
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 bogatyrs were hired to guard Lukomorye for 240 coins. The cunning Uncle Chernomor can divide the bogatyrs into groups of arbitrary sizes (or keep them all in one group) and then distribute the salary 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 get if:

a) Chernomor distributes the salary among the groups however he wants;

b) Chernomor distributes the salary among the groups equally?

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