
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 the function $f(x) = 
\begin{cases} 
x + \frac{1}{x+1} - \frac{1}{2}, & \text{for } x \geq 1,\\
1, & \text{for } x < 1,
\end{cases}$
find the solution set of the inequality $f(6-x^2) > f(x)$.

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