
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
In a sports complex, stations $A, B, C, D, E$ formed the vertices of a regular pentagon. These stations were connected by straight paths. Additionally, on the path from $A$ to $B$ there was a fountain $F$, which was connected to station $C$ by a path perpendicular to the path from $B$ to $E$. Pat and Mat met at station $E$ and decided to sweep some of the paths. Pat swept the path from $E$ to $B$. Mat swept the path from $E$ to $A$ and also from $A$ to $F$.

Determine the difference in the lengths of the paths swept by Pat and Mat.

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