
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
Michel starts with the string \( H M M T \). An operation consists of either replacing an occurrence of \( H \) with \( H M \), replacing an occurrence of \( M M \) with \( M O M \), or replacing an occurrence of \( T \) with \( M T \). For example, the two strings that can be reached after one operation are \( H M M M T \) and \( H M O M T \). Compute the number of distinct strings Michel can obtain after exactly 10 operations.

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