
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 arithmetic sequence $\{a\_n\}$ with a common ratio less than $1$, where $a\_1= \frac {1}{2},7a\_2=2S\_3$.

1. Find the general term formula of the sequence $\{a\_n\}$.
2. Let $b\_n=\log _{2}(1-S\_{n+1})$, if $\frac {1}{b\_1b\_3}+ \frac {1}{b\_3b\_5}+...+ \frac {1}{b\_{2n-1}b\_{2n+1}}= \frac {5}{21}$, find $n$.

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