
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
Given that John added two three-digit positive integers, $x$ and $y$, where the six digits across these numbers must all be different and $x$ contains the digit "0", determine the smallest possible value for the sum of the digits of the three leftmost digits in the total $T$.

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