
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 the function \( f_{0}(x) = |x| \), \( f_{1}(x) = \left| f_{0}(x) - 1 \right| \), \( f_{2}(x) = \left| f_{1}(x) - 2 \right| \). Determine the area of the enclosed region formed by the graph of \( f_{2}(x) \) and the x-axis.

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