
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
Let $p$ be the proposition that the function $y=x^2-4x+1$ is decreasing on the interval $(-\infty, a)$.  
Let $q$ be the proposition that the function $y=\log_{(7-2a)}x$ is increasing on the interval $(0, +\infty)$.  
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}
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