
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
Given that $y$ is a multiple of $30492$, what is the greatest common divisor of $g(y)=(3y+4)(8y+3)(11y+5)(y+11)$ and $y$?

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