
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 that $a\geqslant 1$, and $f(x)=(\sin x-a)(a-\cos x)+\sqrt{2}a$.

(1) Find the range of $f(x)$ when $a=1$;

(2) If the function $f(x)$ has only one zero in the interval $[0,\pi]$, find the range of $a$.

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