
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
Given the sequences \(\{a_{n}\}\) and \(\{b_{n}\}\) with general terms \(a_{n} = 2^{n}\) and \(b_{n} = 5n - 2\), find the sum of all elements in the set \(\{a_{1}, a_{2}, \cdots, a_{2019}\} \cap \{b_{1}, b_{2}, \cdots, b_{2019}\}\).

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