
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
The sides  $AD$  and  $BC$  of a convex quadrilateral  $ABCD$  are extended to meet at  $E$ .  Let  $H$  and  $G$  be the midpoints of  $BD$  and  $AC$ , respectively.  Find the ratio of the area of the triangle  $EHG$  to that of the quadrilateral  $ABCD$ .

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