
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
In the Cartesian coordinate system $xOy$, line 1 is tangent to both the curve $y=x^{2}$ ($x > 0$) and $y=x^{3}$ ($x > 0$), with the points of tangency being $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$, respectively. The value of $\dfrac{x_{1}}{x_{2}}$ is __________.

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