
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 $(a,b,c,d)$ be an ordered quadruple of not necessarily distinct integers, each one of them in the set ${1,2,3,4}.$ For how many such quadruples is it true that $a\cdot d-b\cdot c$ is odd?
A) 48
B) 64
C) 96
D) 128
E) 192

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