
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 \( A B C \) be a triangle. The midpoints of the sides \( B C, A C \), and \( A B \) are denoted by \( D, E \), and \( F \) respectively.

The two medians \( A D \) and \( B E \) are perpendicular to each other and have lengths \( \overline{A D} = 18 \) and \( \overline{B E} = 13.5 \).

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

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