
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 triangle \(ABC\), the side \(BC\) is 19 cm. The perpendicular \(DF\), drawn to side \(AB\) through its midpoint \(D\), intersects side \(BC\) at point \(F\). Find the perimeter of triangle \(AFC\) if side \(AC\) is 10 cm.

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