
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
It is known that a squirrel is hopping in the first quadrant of the coordinate plane $(x \geqslant 0, y \geqslant 0)$. It can jump from point $(x, y)$ to point $(x-5, y+7)$ or to point $(x+1, y-1)$, but it cannot jump out of the first quadrant. From which initial points $(x, y)$ cannot the squirrel jump to a point that is more than 1000 units away from the origin? Draw the set of all such points and find its area.

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