
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 modern conditions, digitalization is considered relevant - the transfer of all information into digital code. Each letter of the alphabet can be assigned a non-negative integer called the letter's code. Then the weight of a word can be defined as the sum of the codes of all the letters in the given word. Is it possible to encode the letters E, O, S, T, Ш, Ь with elementary codes, each consisting of a single digit from 0 to 9, such that the weight of the word "СТО" is not less than the weight of the word "ШЕСТЬСОТ"? If such encoding is possible, in how many ways can it be accomplished? If such encoding is possible, does it allow unique word recovery from its code?

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