
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
Shirley has a magical machine.  If she inputs a positive even integer  $n$ , the machine will output  $n/2$ , but if she inputs a positive odd integer  $m$ , the machine will output  $m+3$ . The machine keeps going by automatically using its output as a new input, stopping immediately before it obtains a number already processed. Shirley wants to create the longest possible output sequence possible with initial input at most  $100$ . What number should she input?

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