
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
A string of digits is defined to be similar to another string of digits if it can be obtained by reversing some contiguous substring of the original string. For example, the strings 101 and 110 are similar, but the strings 3443 and 4334 are not. (Note that a string is always similar to itself.)

Consider the string of digits
\[ S=01234567890123456789012345678901234567890123456789, \]
consisting of the digits from 0 to 9 repeated five times. How many distinct strings are similar to \( S \)?

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