
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 $y= \sqrt{\frac{1+x}{1-x}} + \log(3-4x+x^2)$, its domain is $M$.  
(1) Find $M$;  
(2) When $x \in M$, find the minimum value of $f(x) = 4^x + 2^{x+2}$.

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