
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 by letters (different letters represent different digits). It turns out that all five addends are not integers, but the sum itself is an integer. What exactly is the sum? For each possible answer, provide one example with these five addends. Explain why other sums are not possible.

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