
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 \( f(x) \) be an even function defined on \( \mathbf{R} \) with a period of 2, strictly decreasing on the interval \( [0, 1] \), and satisfying \( f(\pi)=1 \) and \( f(2 \pi)=2 \). Determine the solution set of the system of inequalities:
\[ \left\{\begin{array}{l}
1 \leq x \leq 2, \\
1 \leq f(x) \leq 2
\end{array}\right. \]

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