
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
Determine the zeros and local extrema of the function

$$
y=f(x)=x^{2}-\{x\}^{2}+x+\left|x^{2}-1\right|
$$

(where $\{x\}$ denotes the fractional part of $x$).

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