
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
Given the functions \( f_0(x) = |x| \), \( f_1(x) = \left| f_0(x) - 1 \right| \), and \( f_2(x) = \left| f_1(x) - 2 \right| \), determine the area of the closed region enclosed by the graph of the function \( y = f_2(x) \) and the x-axis.

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