
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 $\triangle ABC$, $\angle C = 90^\circ$, $\angle B = 30^\circ$, and $AC = 1$. Point $M$ is the midpoint of $AB$. The triangle $\triangle ACM$ is folded along $CM$ so that the distance between points $A$ and $B$ is $\sqrt{2}$. Find the distance from point $A$ to the plane $BCM$.

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