
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 that \( f(x) \) is an even function defined on \(\mathbf{R}\), and for any real number \( x \), \( f(x+1) = f(1-x) \) holds true. When \( 1 \leq x \leq 2 \), \( f(x) = \ln x \). If the equation \( f(x) + a x - 1 = 0 \) has two distinct real roots in the interval \( [3, 5] \), what is the range of values for \( a \)?

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