
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 that the sequence $\{a\_n\}$ satisfies $\frac{1}{a_{n+1}} - \frac{1}{a_n} = d (n \in \mathbb{N}^*, d$ is a constant$)$, it is called a harmonic sequence. It is known that the sequence $\{\frac{1}{x\_n}\}$ is a harmonic sequence and $x\_1 + x\_2 + ... + x_{20} = 200$. Find the value of $x\_5 + x_{16}$.

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