
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 $a_{1}, a_{2}, a_{3}, \cdots$ be a non-decreasing sequence of positive integers. For $m \geqslant 1$, define
$$
b_{m}=\min \left\{n \mid a_{n} \geqslant m\right\},
$$
which means $b_{m}$ is the smallest $n$ such that $a_{n} \geqslant m$. Given that $a_{19}=85$, find the maximum value of $a_{1} + a_{2} + \cdots + a_{19} + b_{1} + b_{2} + \cdots + b_{85}$.

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