
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 an even function \( y = f(x) \) defined on \(\mathbf{R}\) that satisfies \( f(x) = f(2 - x) \), and for \( x \in [0, 1] \), \( f(x) = x^2 \), determine the expression for \( f(x) \) when \( 2k - 1 \leqslant x \leqslant 2k + 1 \) (\(k \in \mathbf{Z}\)).

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