
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
A kangaroo is jumping in the quadrant $x \geqslant 0, y \geqslant 0$ of the coordinate plane $Oxy$ in the following manner: from the point $(x, y)$, the kangaroo can jump to the point $(x-5, y+7)$ or to the point $(x+1, y-1)$. However, jumping to points where one of the coordinates is negative is not allowed. From which initial points $(x, y)$ can the kangaroo not reach a point that is more than 1000 units away from the origin? Draw the set of all such points $(x, y)$ and determine its area.

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