
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
Masha, while bored during a math lesson, performed the following operation on a certain 2015-digit natural number: she removed the last digit from its decimal notation, multiplied the resulting number by 3, and added twice the digit she removed. She repeated this operation with the resulting number and so on. After many applications of this operation, the resulting numbers stopped changing, and she then stopped.

a) What number did Masha end up with in the end?

b) What is the smallest number that Masha could have started with (indicate its last two digits)?

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