
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 $A_n=\{x|2^n<x<2^{n+1}, x=3m, m\in\mathbb{N}\}$, if $|A_n|$ represents the number of elements in set $A_n$, then find the value of $|A_5|$ and $|A_1|+|A_2|+|A_3|+\ldots+|A_{10}|$.

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