
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
If a sequence $\{a_n\}$ satisfies $\frac{1}{a_{n+1}} - \frac{1}{a_n} = d$ ($n \in \mathbb{N^*}$, $d$ is a constant), then the sequence $\{a_n\}$ is called a harmonic sequence. Suppose $\{\frac{1}{x_n}\}$ is a harmonic sequence and the sum of the first 22 terms is $x_1 + x_2 + \dots + x_{22} = 77$, find the value of $x_{11} + x_{12}$.

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