
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
Let \( \mathcal{T}_{n} \) be the set of binary strings of length \( n \) such that any 4 adjacent digits sum to at least 2. For example, \( 001100 \) works, but \( 1000001 \) does not. Find the number of elements in \( \mathcal{T}_{9} \).

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