
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 $f(x)=\sin x-a\cos x$, one of its zeros is $\dfrac{\pi}{4}$.
(Ⅰ) Find the value of the real number $a$;
(Ⅱ) Let $g(x)=f(x)\cdot f(-x)+2\sqrt{3}\sin x\cos x$, if $x\in\left[0, \dfrac{\pi}{2}\right]$, find the range of $g(x)$.

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