
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
Richard starts with the string  $HHMMMMTT$ . A move consists of replacing an instance of  $HM$  with  $MH$ , replacing an instance of  $MT$  with  $TM$ , or replacing an instance of  $TH$  with  $HT$ . Compute the number of possible strings he can end up with after performing zero or more moves.

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