
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
Points $P$ and $Q$ are, respectively, the midpoint of one side and one-third of the way across an adjacent side of a square. What fraction of the interior of the square is shaded? The region outside the triangle formed by $P$, $Q$, and the closest vertex to $Q$ is shaded.

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