
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
Define a function \( f(x) \) on \(\mathbf{R}\). Its graph is symmetric with respect to the line \(x=1\) and also satisfies \( f(6-x) = f(x) \). When \( x \in [-1, 1] \), \( f(x) = x^2 - 2x \). Let \( I_k = [4k-1, 4k+3] \) for \( k \in \mathbf{Z} \). If the function \( y = \log_{a} x \) \((a > 0\) and \( a \neq 1)\) has two distinct intersection points with the graph of \( f(x) \) within the interval \( I_k \) for \( k \geqslant 1 \), then the range of values for \( a \) is:

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