
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
Determine the range of values for $a$ such that the propositions $p$ and $q$ meet the following conditions: $p$ states that $a(1-a) > 0$, $q$ states that the parabola $y = x^2 + (2a-3)x + 1$ intersects the x-axis at two distinct points. Both "$p \lor q$" is true and "$p \land q$" is false.

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