
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 propositions $p$: The function $y=x^{2}-2x+a$ has $1$ zero point in the interval $(1,2)$; and proposition $q$: The function $y=x^{2}+(2a-3)x+1$ intersects the $x$-axis at two different points. If $p∧q$ is a false proposition, $p∨q$ is a true proposition, find the range of values for $a$.

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