
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 $f(x)= \sqrt {1-x}$, $g(x)=\sin x \cdot f(\sin 2x)+ \frac { \sqrt {6}+ \sqrt {2}}{4}f(\cos 4x)$, $x\in\left[- \frac {π}{4},0\right]$
(1) Simplify the function $g(x)$ into the form of $A\sin (ωx+φ)+B(A,B∈R,ω > 0,φ∈(-π,π))$;
(2) Find the range of the function $g(x)$.

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