
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 have lengths $\overline{AD}=18$ 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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