
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
For the sequence $\{a_{n}\}$, let $T_{n}=a_{1}-a_{2}+a_{3}-a_{4}+\cdots +\left(-1\right)^{n+1}a_{n}$, the following four conclusions are given:<br/>① If $a_{n}=n$, then $T_{2023}=1012$;<br/>② If $T_{n}=n$, then $a_{2022}=-1$;<br/>③ There exists a sequence $\{a_{n}\}$ with all integer terms, such that $|T_{n}| \gt |T_{n+1}|$ holds for any $n\in N^{*}$;<br/>④ If for any $n\in N^{*}$, $|T_{n}| \lt M$, then $|a_{n+1}-a_{n}| \lt 2M$.<br/>The correct conclusions are those with the following numbers: ____.

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