
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 \( a_{1}, a_{2}, \cdots, a_{n}, \cdots \) be a non-decreasing sequence of positive integers. For \( m \geqslant 1 \), define \( b_{m}=\min \left\{n ; a_{n} \geqslant m\right\} \), i.e., \( b_{m} \) is the smallest value of \( n \) 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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