
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 sequence $\{a_n\}$ that satisfies $\dfrac{1}{{a_{n+1}}} - \dfrac{1}{{a_n}} = d$ ($n \in \mathbb{N}^*$), where $d$ is a constant, and the sequence $\left\{ \dfrac{1}{{x_n}}\right\}$ is a harmonic sequence with $x_1 + x_2 + \ldots + x_{20} = 200$, find the value of $x_5 + x_{16}$.

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