
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 midpoints of the sides of a convex pentagon are successively connected by line segments. Find the perimeter of the resulting pentagon, given that the sum of all the diagonals of the original pentagon is \(a\).

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