
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 $\mathrm{O}$ be the intersection point of the diagonals of a convex quadrilateral $A B C D$, and let $P, Q, R$, and $S$ be the centroids of triangles $A O B$, $B O C$, $C O D$, and $D O A$, respectively. Find the ratio of the areas of the quadrilateral $P Q R S$ to that of $A B C D$.

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