
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
Elsa wrote the numbers $1, 2, \ldots, 8$ on the board. She then allows herself operations of the following form: she selects two numbers $a$ and $b$ such that $a+2 \leq b$, if such numbers exist, then she erases them, and writes the numbers $a+1$ and $b-1$ in their place.

(a) Demonstrate that Elsa must stop after a finite number of operations.

(b) What is the maximum number of operations Elsa can perform?

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