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

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