
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
Let  $r$ ,  $s$  be real numbers, find maximum  $t$  so that if  $a_1, a_2, \ldots$  is a sequence of positive real numbers satisfying
\[ a_1^r + a_2^r + \cdots + a_n^r \le 2023 \cdot n^t \]
for all  $n \ge 2023$  then the sum
\[ b_n = \frac 1{a_1^s} + \cdots + \frac 1{a_n^s} \]
is unbounded, i.e for all positive reals  $M$  there is an  $n$  such that  $b_n > M$ .

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