
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
The theater company organizer wants to arrange the cast members in a perfect formation that includes all members with no spaces left unoccupied. When arranged in a perfect square formation, there are 3 members leftover. If arranged in a formation with 9 more rows than columns, the organizer can perfectly allocate every member to a position without any left over. Determine the maximum number of members this company can have.

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