
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
Proposition p: The inequality $x^2 + 2ax + 4 > 0$ holds for all $x \in \mathbb{R}$, and proposition q: The function $f(x) = (3 - 2a)^x$ is an increasing function. If either p or q is true, but not both, find the range of the real number $a$.

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