
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 right-angled triangle \( ABC \) with \(\angle ACB = 90^\circ\), \( AC = 6 \), and \( BC = 4 \), a point \( D \) is marked on the line \( BC \) such that \( CD > BD \) and \(\angle ADC = 45^\circ\). A point \( E \) is marked on the line \( AD \) such that the perimeter of the triangle \( CBE \) is the smallest possible. Then, a point \( F \) is marked on the line \( DC \) such that the perimeter of the triangle \( AFE \) is the smallest possible. Find \( CF \).

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