
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 $xOy$, a polar coordinate system is established with the origin O as the pole and the positive half-axis of the x-axis as the polar axis. Curve $C_1$ is given by the parametric equations $x = 4 + t$, $y = 5 + 2t$ (where $t$ is the parameter), and curve $C_2$ by the polar equation $\rho^2 - 6\rho\cos\theta - 10\rho\sin\theta + 9 = 0$.  
(I) Convert curve $C_1$ into an implicit Cartesian equation and curve $C_2$ into a parametric equation.  
(II) Determine the positional relationship between curves $C_1$ and $C_2$.

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