
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
Two ordered pairs \((a, b)\) and \((c, d)\), where \(a, b, c, d\) are real numbers, form a basis of the coordinate plane if \(ad \neq bc\). Determine the number of ordered quadruples \((a, b, c, d)\) of integers between 1 and 3 inclusive for which \((a, b)\) and \((c, d)\) form a basis for the coordinate plane.

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