
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
Write a sine function that satisfies the following conditions: $f\left(x\right)=\_\_\_\_\_\_.$  
$(1)$ The smallest positive period is $\pi$;  
$(2)$ $f\left(x\right)$ is monotonically increasing on $[{0,\frac{π}{4}}]$;  
$(3)$ For all $x\in R$, there exists $x_{0}$ such that $f\left(x\right)\leqslant f(x_{0})=2$.

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