
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
Consider an arithmetic sequence with common ratio $c$ and first term $a\_1=1$. The sequence satisfies $a\_n=\frac{a_{n-1}+a_{n-2}}{2}$ for all $n \geq 3$.
(I) Find the value of $c$;
(II) Find the sum $S\_n$ of the first $n$ terms of the sequence ${na\_n}$.

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