
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 a sequence $\{a_n\}$: 3, 5, 6, ... which is the set $\{x | x = 2^s + 2^t, 0 \leq s < t, s, t \in \mathbb{Z}\}$ arranged in ascending order, then  
(1) Find $a_5 = \_\_\_\_\_\_$;  
(2) If $a_n = 16640$, then find the value of $n = \_\_\_\_\_\_$.

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