
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
The opening of a pit is a circle with a diameter of $100 \mathrm{~m}$, and its cross-sections passing through the center of the circle are equilateral triangles. Let $A$ and $B$ be two diametrically opposite points on the opening, $C$ the deepest point of the pit, and $H$ the midpoint of $BC$. What is the length of the shortest path connecting $A$ with $H$?

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