
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
Suppose $a_{1}, a_{2}, \cdots, a_{n}, \cdots$ is a non-decreasing sequence of positive integers. For $m \geq 1$, define $b_{m}=\min \left\{n \mid a_{n} \geq m\right\}$, which means $b_{m}$ is the smallest $n$ such that $a_{n} \geq m$. Given $a_{19}=85$, find the maximum value of
$$
a_{1}+a_{2}+\cdots+a_{19}+b_{1}+b_{2}+\cdots+b_{85}
$$
(1985 USAMO problem).

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