
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 $a_1=1$, $a_2+a_4=6$, and for any $n∈N^{*}$, the function $f(x)=(a_n-a_{n+1}+a_{n+2})x+a_{n+1}\cdot\cos x-a_{n+2}\sin x$ satisfies $f'( \frac {\pi}{2})=0$, find the sum $S_n$ of the first $n$ terms of the sequence $\{c_n\}$, where $c_n=a_n+\frac{1}{2^{a_n}}$.

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