
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 first term of an arithmetic sequence $\\{ {a}_{n} \\}$ is $1$, and the common difference is $2$. If ${a}_{1}{a}_{2}-{a}_{2}{a}_{3}+{a}_{3}{a}_{4}-{a}_{4}{a}_{5}+⋯-{a}_{2n}{a}_{2n+1} \geqslant t\cdot{n}^{2}$ holds for all positive integers $n$, then the range of the real number $t$ is ________.

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