
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
How many four-digit integers $abcd$, with $a \neq 0$, have the property such that the digits $a, b, c,$ and $d$ are non-repeating and $ab$, $bc$ and $cd$ (where $ab = 10a+b$, $bc = 10b+c$, $cd = 10c+d$) form an increasing geometric sequence? One such number is $1324$, where $a=1$, $b=3$, $c=2$, and $d=4$.
A) 5  
B) 8  
C) 10  
D) 13  
E) 16

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