
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 $f(x) = 2^{2x} - 2^{x+1} + 2$, with its domain as $M$ and its range as $[1, 2]$, the correct statement(s) among the following is/are  
(1) $M = [0, 2]$; (2) $M = (-\infty, 1]$; (3) $M \subseteq (-\infty, 1]$; (4) $0 \in M$; (5) $1 \in M$.

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