
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  $ABCD$  be a rhombus with angle  $\angle A = 60^\circ$ . Let  $E$  be a point, different from  $D$ , on the line  $AD$ . The lines  $CE$  and  $AB$  intersect at  $F$ . The lines  $DF$  and  $BE$  intersect at  $M$ . Determine the angle  $\angle BMD$  as a function of the position of  $E$  on  $AD.$ 

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