
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
In a regular quadrilateral pyramid \( S A B C D \) where each edge is equal to 2, a cross-section is constructed by a plane that is parallel to the base diagonal \( A C \) and the lateral edge \( S B \), and intersects the edge \( A B \). Find the perimeter of the polygon formed by this cross-section, given that the lower base of the cross-section is \( \sqrt{2} \).

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