
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}\}\\) that satisfies \\(\sqrt {a_{1}} + \sqrt {a_{2}} + \ldots + \sqrt {a_{n}} = 2^{n+1}\\), let the sum of the first \\(n\\) terms of \\(\{a_{n}\}\\) be \\(S_{n}\\). Find the value of \\(\frac{3}{16}S_{n}\\).

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