
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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Each of the lateral sides \(AB\) and \(CD\) of trapezoid \(ABCD\) is divided into five equal parts. Let \(M\) and \(N\) be the second division points on the lateral sides, counting from vertices \(B\) and \(C\) respectively. Find the length of \(MN\), given that the bases \(AD = a\) and \(BC = b\).

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