
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
Three non-overlapping regular polygons, at least two of which are congruent and one is a square, all have sides of length $2$. The polygons meet at a point in such a way that the sum of the three interior angles at the point is $360^{\circ}$. Determine the largest possible perimeter of the polygon formed by these three polygons.

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