
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
The correct statements are ______. (Select the serial number)<br/>① If $\left(x-1\right)^{x-1}=1$, then there are $3$ values of $x$ that satisfy the condition.<br/>② If $x=3^{2m-2}$ and $y=3-9^{m}$, then $y$ can be expressed as an algebraic expression containing $x$ as $y=-9x+3$.<br/>③ Given $\left(x-20\right)^{2}+\left(x-28\right)^{2}=100$, the value of $\left(x-24\right)^{2}$ is $34$.<br/>④ Among the numbers $1$, $2$, $3$, $\ldots $, $58$, there are $14$ numbers that cannot be represented as the difference of squares of two natural numbers.

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