
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 a right triangle $ABC$, with $\angle C = 90^\circ$, altitude $CD$ is drawn from $C$ to hypotenuse $AB$. Medians are also drawn from vertices $A$ to $BD$ and from $B$ to $AD$. Given that the median from $A$ has a length of $7$ units and the median from $B$ has a length of $4\sqrt{2}$ units, and the altitude has a length of $4$ units, determine the length of side $AB$.

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