
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 an increasing geometric sequence $\{a\_n\}$, it is known that $a\_2+a\_3+a\_4=28$, and $a\_3+2$ is the arithmetic mean of $a\_2$ and $a\_4$.
(1) Find $a\_n$.
(2) Let $b\_n=\log \_{ \frac {1}{2}}a\_n$ and $S\_n=b\_1+b\_2+...+b\_n$, find $S\_n$.

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