
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 triangle $ABC$, with $\angle BAC = 90^\circ$, $AB=AC=1$, point $M$ is the midpoint of hypotenuse $BC$. Point $D$ is on $AC$ such that $MD$ is perpendicular to $AC$. If $AD = x$, find $MD$.
A) $\frac{\sqrt{2}}{2}$
B) $\sqrt{\frac{1}{2} - x^2}$
C) $\sqrt{1 - x^2}$
D) $\frac{1}{2}$

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