
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
Let $E$ be the perpendicular projection of vertex $A$ of the parallelogram $ABCD$ onto line $CB$, and let $F$ be the perpendicular projection onto line $CD$. Let $M$ be the orthocenter of triangle $AEF$. Determine the length of segment $AM$ given the lengths of segments $AC$ and $EF$, and the angle of inclination between lines $AC$ and $EF$.

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