
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 proposition P: The function $f(x) = \log_{2m}(x+1)$ is an increasing function, and proposition Q: $\forall x \in \mathbb{R}, x^2 + mx + 1 \geq 0$, if "P ∨ Q" (P or Q) is a true proposition and "P ∧ Q" (P and Q) is a false proposition, find the range of the real number $m$.

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