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

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