
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 $$\frac {1}{a_{n+1}}- \frac {1}{a_{n}}=d$$ (where $n\in\mathbb{N}^*$, $d$ is a constant), then the sequence $\{a_n\}$ is called a "harmonic sequence". Given that the sequence $\{\frac {1}{x_{n}}\}$ is a "harmonic sequence", and $x_1+x_2+\ldots+x_{20}=200$, the maximum value of $x_3x_{18}$ is \_\_\_\_\_\_.

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