
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 that the three two-digit integers $ab<bc<cd$ form an increasing arithmetic sequence, where each pair of consecutive numbers has a difference of exactly 5? For example, if $ab = 12$, then $bc = 17$ and $cd = 22$.
A) 0
B) 2
C) 5
D) 10
E) 15

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