
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
Mathematicians found that when studying the reciprocals of the numbers $15$, $12$, and $10, it was discovered that $\frac{1}{12}-\frac{1}{15}=\frac{1}{10}-\frac{1}{12}$. Therefore, they named three numbers with this property as harmonic numbers, such as $6$, $3$, and $2$. Now, given a set of harmonic numbers: $x$, $5$, $3$ $(x>5)$, what is the value of $x$?

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