
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 sets $P=\{x|x=2^n, n\in\mathbb{N}\}$ and $Q=\{x|x=2n, n\in\mathbb{N}\}$, arrange all elements of $P\cup Q$ in ascending order to form a sequence $\{a_n\}$. Calculate the sum of the first 20 terms of $\{a_n\}$, denoted as $S_{20}$.

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