
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 a polar coordinate system, the equation of curve C<sub>1</sub> is given by $\rho^2 - 2\rho(\cos\theta - 2\sin\theta) + 4 = 0$. With the pole as the origin and the polar axis in the direction of the positive x-axis, a Cartesian coordinate system is established using the same unit length. The parametric equation of curve C<sub>2</sub> is given by 
$$
\begin{cases}
5x = 1 - 4t \\
5y = 18 + 3t
\end{cases}
$$
where $t$ is the parameter.
(Ⅰ) Find the Cartesian equation of curve C<sub>1</sub> and the general equation of curve C<sub>2</sub>.
(Ⅱ) Let point P be a moving point on curve C<sub>2</sub>. Construct two tangent lines to curve C<sub>1</sub> passing through point P. Determine the minimum value of the cosine of the angle formed by these two tangent lines.

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