
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  $\triangle ABC$ , point  $D$  lies on side  $AC$  such that  $\angle ABD=\angle C$ . Point  $E$  lies on side  $AB$  such that  $BE=DE$ .  $M$  is the midpoint of segment  $CD$ . Point  $H$  is the foot of the perpendicular from  $A$  to  $DE$ . Given  $AH=2-\sqrt{3}$  and  $AB=1$ , find the size of  $\angle AME$ .

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