
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
Three numbers, each with three digits, represented by different letters (${a, b, c, d, e, f}$), are vertically aligned and summed. If each letter represents a different digit, find the value of $a+b+c+d+e+f$ given the following setup:
```
  a b c
  d e a
+ f a b
---------
  1 1 1 1
```
This puzzle assumes digits cannot repeat and digits add up as per usual arithmetic rules, with carrying over if the sum exceeds 9.

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