
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 square of side  $a$ . On side  $AD$  consider points  $E$  and  $Z$  such that  $DE=a/3$  and  $AZ=a/4$ . If the lines  $BZ$  and  $CE$  intersect at point  $H$ , calculate the area of the triangle  $BCH$  in terms of  $a$ .

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