
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 some competitive events, a participant's final score is the arithmetic mean of all previous rounds' scores. The students know this fact: in all rounds' scores, if some high scores are removed in descending order, the average score decreases; conversely, if some low scores are removed in ascending order, the average score increases. These two facts can be described using mathematical language as follows: Given a finite sequence a₁, a₂, …, aₙ that satisfies a₁ ≤ a₂ ≤ … ≤ aₙ, and not all a₁, a₂, …, aₙ are equal, then ①_______; ②_______.

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