
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
After an exam, if you remove some high scores in sequence, the class average will decrease; conversely, if you remove some low scores in sequence, the class average will increase. These two facts can be mathematically described as follows: If the finite sequence \(a_{1}, a_{2}, \cdots, a_{n}\) satisfies \(a_{1} \leqslant a_{2} \leqslant \cdots \leqslant a_{n}\), then (conclusion expressed as a mathematical formula).

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