
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 a certain tribe's language, any sequence of 10 digits made up of 0s and 1s is considered a word. Two words are synonyms if and only if one word can be obtained from the other by performing the following operation: remove a consecutive sequence of digits whose sum is even, then write the removed digits back in reverse order. How many distinct words are there in the language of this tribe?

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