
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 propositions p: "The curve corresponding to the equation $x^2 + y^2 - x + y + m = 0$ is a circle" and q: "The function $f(x) = \lg(mx^2 - 4x + m)$ has the domain $\mathbb{R}$". If only one of these two propositions is true, determine the range of the real number $m$.

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