
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
Let \( ABC \) be a triangle. The midpoints of the sides \( BC \), \( AC \), and \( AB \) are denoted by \( D \), \( E \), and \( F \), respectively.

The two medians \( AD \) and \( BE \) are perpendicular to each other, and their lengths are \( \overline{AD} = 18 \) and \( \overline{BE} = 13.5 \).

Calculate the length of the third median \( CF \) of this triangle.

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