
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
Consider two equiangular polygons, $A_1$ and $A_2$, where each interior angle of $A_1$ is $y$ degrees and each interior angle of $A_2$ is $ly$ degrees, with $l > 1$ being an integer. If $y$ is a multiple of $30$ degrees, find how many pairs $(y, l)$ satisfy the conditions given that both $y$ and $ly$ correspond to possible polygon interior angles.
**A)** 0
**B)** 1
**C)** 2
**D)** 3

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