
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
Let $y=f\left(x\right)$ have a derivative $y={f'}\left(x\right)$ on $R$. For any $x\in R$, $f\left(x\right)-f\left(-x\right)=2\sin x$, and on $\left(0,+\infty \right)$, ${f'}\left(x\right) \gt \cos x$. If $f({\frac{π}{2}-t})-f(t) \gt \cos t-\sin t$, then the range of real number $t$ is ______.

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