
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
a) Two circles with the same radius of 13 intersect at points \(A\) and \(B\). Point \(C\) is chosen on the first circle, and point \(D\) is chosen on the second circle. It turns out that point \(B\) lies on segment \(CD\), and \(\angle CAD = 90^\circ\). On the perpendicular to \(CD\) passing through point \(B\), point \(F\) is chosen such that \(BF = BD\) (points \(A\) and \(F\) are on the same side of line \(CD\)). Find the length of segment \(CF\).

b) Additionally, suppose that \(BC = 10\). Find the area of triangle \(ACF\).

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