
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]


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The base of pyramid \( SABC \) is a right triangle \( ABC \). The edge \( SA \) is perpendicular to the base plane, with \( |SA| = |AB| = |BC| = a \). A cutting plane is passed through the midpoint of edge \( AB \), perpendicular to edge \( SC \), and we need to find the area of the resulting cross-section.

Given: \( SABC \) is a pyramid with vertex \( S \), \( [SA] \perp (ABC) \), \( [AB] \perp [BC] \), \( |SA| = |AB| = |BC| = a \), \( |AM| = |BM| \), and the cross-section \( (MKLN) \) is perpendicular to \( (SC) \).

Find: \( S_{MKLN} \).

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