
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 the domain of the function \( f(x) \) is \( x \in \mathbf{R} \), except \( x \neq 1 \), and \( f(x+1) \) is an odd function, with the additional information that \( f(x) = 2x^2 - x + 1 \) when \( x<1 \), find the interval where \( f(x) \) is decreasing when \( x>1 \).

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