
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
Each of the positive integers \(a, b\), and \(c\) has three digits, and for each of these integers the first digit is the same as its last digit. Also \(b = 2a + 1\) and \(c = 2b + 1\). How many possibilities are there for the integer \(a\)?

A) 0

B) 1

C) 2

D) 3

E) more than 3

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