
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 the sequence $\{a\_n\}$ that satisfies: $a\_1=1$, $a\_{n+1}+2a\_n=0$.
(I) Find the general term formula and the sum of the first n terms $S\_n$;
(II) If the arithmetic sequence $\{b\_n\}$ satisfies $b\_1=a\_4$, $b\_2=a\_2\-a\_3$, find the value of $b\_{37}$ and determine which term in $\{a\_n\}$ is equal to $b\_{37}$?

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