
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
Let  $T=\text{TNFTPP}$ .  Let  $R$  be the region consisting of the points  $(x,y)$  of the cartesian plane satisfying both  $|x|-|y|\leq T-500$  and  $|y|\leq T-500$ .  Find the area of region  $R$ .

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