
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
Given a binary string \( S \) of length \( 10^4 \) containing only '0' and '1'. A \( k \)-block of \( S \) is defined as a contiguous substring of \( S \) of length \( k \). Two \( k \)-blocks \( a_1a_2 \cdots a_k \) and \( b_1b_2 \cdots b_k \) are considered identical if and only if \( a_i = b_i \) for \( i = 1, 2, \cdots, k \).

Consider all binary strings of length \( 10^4 \) that contain at most seven different 3-blocks. Determine the maximum number of distinct 10-blocks that such a string can contain.

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