
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
A prism $A B C A_1 B_1 C_1$ is given. Construct the image of the point $M$ where the planes $A_1 B C$, $A B_1 C$, and $A B C_1$ intersect. Let the height of the prism be $h$. Find the distance from point $M$ to the bases of the prism.

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