
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
The absolute value of a number \( x \) is equal to the distance from 0 to \( x \) along a number line and is written as \( |x| \). For example, \( |8|=8, |-3|=3 \), and \( |0|=0 \). For how many pairs \( (a, b) \) of integers is \( |a|+|b| \leq 10 \)?

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