
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 side \( AB \) of the trapezoid \( ABCD \) is divided into five equal parts, and through the third division point, counting from point \( B \), a line is drawn parallel to the bases \( BC \) and \( AD \). Find the segment of this line that is enclosed between the sides of the trapezoid, given \( BC = a \) and \( AD = b \).

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