
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

On the side \( AC \) of an equilateral triangle \( ABC \), a point \( D \) is marked. On the segments \( AD \) and \( DC \), equilateral triangles \( ADE \) and \( DCF \) are constructed outward from the original triangle. It is known that the perimeter of triangle \( DEF \) is 19, and the perimeter of pentagon \( ABCEF \) is 43.

(a) Find the length of segment \( AB \).

(b) Find the length of segment \( EF \).

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