
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]


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Given the operation rule for a second-order determinant $|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|=ad-bc$, and the inequality $|\begin{array}{l}{2}&{3-x}\\{1}&{x}\end{array}| > 0$, determine the range of values for $x$.

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