
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 harmonic mean of the first n terms of the sequence $\left\{{a}_{n}\right\}$ is $\dfrac{1}{2n+1}$, and ${b}_{n}= \dfrac{{a}_{n}+1}{4}$, find the value of $\dfrac{1}{{b}_{1}{b}_{2}}+ \dfrac{1}{{b}_{2}{b}_{3}}+\ldots+ \dfrac{1}{{b}_{10}{b}_{11}}$.

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