
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 \( R \) be the reals and \( C \) the set of all functions \( f : [0, 1] \to R \) with a continuous derivative and satisfying \( f(0) = 0 \) and \( f(1) = 1 \). Find \( \inf_{f \in C} \int_{0}^{1} | f'(x) - f(x) | \, dx \).

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