
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
Two two-digit, positive integers \( a \) and \( b \) are given, such that:
1) One number is greater than the other by 14.
2) They share one identical digit in their decimal representation.
3) The sum of the digits of one number is twice the sum of the digits of the other number.
Find these numbers.

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