
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) Start the game with the number 45 and show one way to proceed until reaching the number 1.

b) Start the game with the number 345 and show one way to proceed until reaching the number 1.

c) Explain how to reach the number 1 by starting the game with any natural number other than zero.

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