
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
Consider two propositions: ① The solution set of the inequality $mx^2 + 1 > 0$ with respect to $x$ is $\mathbb{R}$; ② The function $f(x) = \log(mx)$ is a decreasing function. If there is exactly one true proposition among these two, then the range of the real number $m$ is $\boxed{m \geq 1 \text{ or } m = 0}$.

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