
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 inequality $x^2 - 2ax + 4 > 0$ holds for all $x \in \mathbb{R}$; proposition q: The function $y = \log_{(4-2a)}x$ is decreasing on $(0, +\infty)$. If $p \lor q$ is true and $p \land q$ is false, find the range of the real number $a$.

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