
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 language of the Tru-la-la tribe, any sequence of 10 digits consisting of 0s and 1s is considered a word. Two words are defined as synonyms if and only if one can be obtained from the other through a series of operations where a sequence of consecutive digits, whose sum is even, is removed and then reinserted at the same position but in the reverse order. How many distinct words with different meanings can be written in the Tru-la-la tribe's language?

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