
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
11 adults and $n$ children played a game of catching Pokémon. Together, they caught $n^{2}+3n-2$ Pokémon, with each adult catching the same amount, and each child catching the same amount, which is 6 less than what each adult caught. How many children participated in the game?

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