
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 in the first quadrant \( x \geq 0, y \geq 0 \) can jump from a point \((x, y)\) to either the point \((x+1, y-1)\) or the point \((x-5, y+7)\) if these points are also in the first quadrant. Which points in the first quadrant are such that the kangaroo cannot reach at least 1000 units away from the origin?

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