
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
Four non-overlapping regular plane polygons, at least two of which are congruent, all have sides of length $1$. The polygons meet consecutively at a central point $A$ such that they form a continuous path around $A$ with the sum of the four interior angles at $A$ being $360^{\circ}$. Calculate the largest possible perimeter that the external boundary of these polygons can have.

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