
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 \(a\) and \(b\). The trapezoid can be cut by a line parallel to the bases such that circles can be inscribed in the two resulting smaller trapezoids. What is the perimeter of the original trapezoid?

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