
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 the right-angled triangle $ABC$, the median to the leg $AC$ is perpendicular to the median to the hypotenuse $AB$. Express the length of the median to $AC$ as a function of $BC = a$.

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