
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 right triangle $ABC$, $\angle C=90^\circ$, and $a$, $b$, $c$ are the sides opposite to $\angle A$, $\angle B$, $\angle C$ respectively. $a$ and $b$ are the roots of the equation $x^2 - 7x + c + 7 = 0$ related to $x$. Find the length of the median to the side $AB$.

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