
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 diagonals of a convex pentagon \(ABCDE\) intersect to form a pentagon \(A_1B_1C_1D_1E_1\) and a five-pointed star.

a) Find the sum of the angles of this star at the vertices \(A\), \(B\), \(C\), \(D\), and \(E\).

b) Find the ratio of the area of pentagon \(A_1B_1C_1D_1E_1\) to the area of pentagon \(ABCDE\), assuming the latter is a regular pentagon.

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