
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 convex quadrilateral. For each triangle formed by taking three of the quadrilateral's vertices, define new points $G^*_A,$ $G^*_B,$ $G^*_C,$ $G^*_D$ on each side of triangles $BCD,$ $ACD,$ $ABD,$ $ABC,$ respectively, dividing each side of these triangles in the ratio 1:4. Calculate the ratio of the area of quadrilateral $G^*_A G^*_B G^*_C G^*_D$ to the area of quadrilateral $ABCD$.

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