
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 convex quadrilateral \(ABCD\), the midpoints of the sequential sides are marked as \(M, N, K, L\). Find the area of the quadrilateral \(MNKL\) if \(|AC| = |BD| = 2a\) and \(|MK| + |NL| = 2b\).

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