
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 BAC as the right angle, let M be a point on side AC such that AM = x. If BC = 2d and AC = h, and we know the sum of distances BM and MC equals the length of the hypotenuse AB, find the value of x.
A) $\frac{h + \sqrt{h^2 - 8d^2}}{2}$
B) $\frac{h - \sqrt{h^2 - 8d^2}}{2}$
C) $\frac{h + 2d}{2}$
D) $\frac{h - 2d}{2}$
E) $\frac{h}{2}$

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