
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
$ABCDE$ is a square-based pyramid where $ABCD$ is the square base and $E$ is the apex of the pyramid. If the edge lengths of the square base are 2 units and the slant height $AE$ is also 2 units, and $M$ is the midpoint of $\overline{CD}$, then what is $\cos \angle AME$?

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