
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

In the sum

$$
\text { П,Я + Т,Ь + Д,Р + О,Б + Е,Й }
$$

all digits are encoded with letters (different letters represent different digits). It turned out that all five addends are not integers, but the sum itself is an integer. What integer is it? For each possible answer, provide an example with such five addends. Explain why other sums cannot be obtained.

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