
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
Given the function $f(x)=x^{2}-x\sin x-\cos x$.  
$(1)$ Find the equation of the tangent line to the curve $y=f(x)$ at the point $\left(0,f(0)\right)$;  
$(2)$ Determine the number of zeros of the function $f(x)$;  
$(3)$ If for any $x∈[0,\frac{π}{2}]$, $ax^{2}-x\sin x-\cos x+a\geqslant 0$ always holds, find the range of values for $a$.

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