
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 proposition $p$ be: The equation $x^2 - x + a^2 - 6a = 0$ has one positive root and one negative root.    
Let proposition $q$ be: The graph of the function $y = x^2 + (a-3)x + 1$ has common points with the x-axis. If the proposition "$p \lor q$" is true, and the proposition "$p \land q$" is false, find the range of values for the real number $a$.

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