
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 $f(x)$ have a derivative $f'(x)$ on $R$, and $g(x) = f(x) - \sin x$ is an even function. Given that on $\left[0,+\infty \right)$, $f'(x) > \cos x$. If $f\left(\frac{π}{2}-t\right) - f(t) > \cos t - \sin t$, determine the range of the real number $t$.

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