
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]


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Given that $\frac{n}{p\_1+p\_2+...+p\_n}$ is the "harmonic mean" of $n$ positive numbers $p\_1$, $p\_2$, ..., $p\_n$, and the harmonic mean of the first $n$ terms of the sequence $\{a\_n\}$ is $\frac{1}{n}$, determine the value of $\frac{1}{a\_1a\_2} + \frac{1}{a\_2a\_3} + ... + \frac{1}{a\_10a\_11}$.

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