
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 proposition P: "For all $x \in \mathbb{R}$, there exists an $m \in \mathbb{R}$ such that $4^x - 2^{x+1} + m = 0$", if the negation of proposition P is false, then the range of the real number $m$ is ____.

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