
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 \( f_0(x) = |x| \), \( f_1(x) = \left| f_0(x) - 1 \right| \), \( f_2(x) = \left| f_1(x) - 2 \right| \), \ldots, \( f_n(x) = \left| f_{n-1}(x) - n \right| \). The function \( f_n(x) \) has exactly two common points with the x-axis. What is the area enclosed by this function curve and the x-axis?

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