
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 even function $y=f\left(x\right)$ is monotonically increasing on the interval $\left[-1,0\right]$, and satisfies $f\left(1-x\right)+f\left(1+x\right)=0$, make the following judgments:<br/>①$f\left(-3\right)=0$; ②$f\left(x\right)$ is increasing on $\left[1,2\right]$; ③The graph of $f\left(x\right)$ is symmetric about the line $x=1$; ④The function $f\left(x\right)$ attains a minimum value at $x=2$; ⑤The function $y=f\left(x\right)$ has no maximum value. The correct judgments are ____.

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