
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
Triangle  $ABC$  has  $\angle{A}=90^{\circ}$ ,  $AB=2$ , and  $AC=4$ . Circle  $\omega_1$  has center  $C$  and radius  $CA$ , while circle  $\omega_2$  has center  $B$  and radius  $BA$ . The two circles intersect at  $E$ , different from point  $A$ . Point  $M$  is on  $\omega_2$  and in the interior of  $ABC$ , such that  $BM$  is parallel to  $EC$ . Suppose  $EM$  intersects  $\omega_1$  at point  $K$  and  $AM$  intersects  $\omega_1$  at point  $Z$ . What is the area of quadrilateral  $ZEBK$ ?

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