
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 $Q$ lie on the sides of a rectangle such that $P$ is $\frac{1}{3}$ the length from one corner along one long side, and $Q$ is at the midpoint of the opposite long side. If a diagonal is drawn from corner to corner passing through $P$ and $Q$, find the fraction of the total area of rectangle that lies below this diagonal. Assume the long side of the rectangle is twice the length of the shorter side.

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