
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
In a Mathematics class, the teacher starts a game by writing a number on the blackboard. To continue the game, the students must write another number, following the rules below:

- If the written number has only one digit, it should be multiplied by 2.
- If the written number has more than one digit, the students can choose to either erase the unit digit or multiply the number by 2.

After the students write a new number, the game continues with this number, always following the same rules. Here are two examples of this game, one starting with 203 and the other with 4197:

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

b) Now start the game with the number 345 and show a way to proceed until reaching 1.

c) Explain how to reach 1 starting the game with any non-zero natural number.

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