
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
There are two four-digit numbers A and B. The common logarithm of A is \(a + \lg b\), where \(a\) and \(b\) are non-zero digits. The sum of the thousand's place digit and the unit's place digit of B is \(\frac{5}{2} b\), and B is \(5b + 1\) less than half of A. Find these two four-digit numbers.

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