
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
In the plane region \(\{(x, y) \mid |x| \leq 1, |y| \leq 1\}\), it is always true that \(a x - 2 b y \leq 2\), calculate the area of the region formed by the moving point \(P(a, b)\).

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