
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
In the sequences $\{a_n\}$ and $\{b_n\}$, it is given that $a_{n+1}=a_n+b_n+ \sqrt{a_n^2+b_n^2}$, $b_{n+1}=a_n+b_n- \sqrt{a_n^2+b_n^2}$, with $a_1=1$ and $b_1=1$. Let $c_n=2^n\left( \frac{1}{a_n}+ \frac{1}{b_n} \right)$, then the sum of the first $n$ terms of the sequence $\{c_n\}$ is ______.

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