
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 equal radii of 17 intersect at points \( A \) and \( B \). Point \( C \) is chosen on the first circle, and point \( D \) 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 \( B \), a point \( F \) is chosen such that \( BF = BD \). Points \( A \) and \( F \) are on opposite sides of the line \( CD \). Find the length of segment \( CF \).

b) Suppose it is additionally known that \( BC = 16 \). Find the area of triangle \( ACF \).

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