
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

Vector $\overrightarrow{OA} = (1,0)$ and vector $\overrightarrow{OB} = (1,1)$, with $O$ being the origin. A point $P(x, y)$ satisfies:

\[
\begin{cases}
0 \leqslant \overrightarrow{OP} \cdot \overrightarrow{OA} \leqslant 1, \\
0 \leqslant \overrightarrow{OP} \cdot \overrightarrow{OB} \leqslant 2,
\end{cases}
\]

Find the area of the shape formed by point $Q(x+y, y)$.

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