
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 $f(x)= \sqrt { \frac {2-x}{3+x}}+\ln (3^{x}- \frac {1}{3})$ with domain $M$.
(1) Find $M$;
(2) When $x \in M$, find the range of $g(x)=4^{x+ \frac {1}{2}}-2^{x+2}+1$.

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