
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
Find the areas of the three polygons described by the following conditions (a), (b), and (c), respectively.
(a) The system of inequalities \( |x| \leq 1 \) and \( |y| \leq 1 \).
(b) The inequality \( |x| + |y| \leq 10 \).
(c) The inequality \( |x| + |y| + |x+y| \leq 2020 \).

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