
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
Medians are drawn from point $A$ and point $B$ in a right triangle to divide segments $\overline{BC}$ and $\overline{AC}$ in half, respectively. The lengths of the medians are 5 and $3\sqrt{5}$ units, respectively. Determine how many units are in the length of segment $\overline{AB}$.

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