
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
The bases of a trapezoid are equal to \(a\) and \(b\) (\(a > b\)). The segments connecting the midpoint of the longer base with the ends of the shorter base intersect the diagonals of the trapezoid at points \(M\) and \(N\). Find \(MN\).

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