
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 $xOy$, the parametric equation of curve $C_{1}$ is given by 
$$
\begin{cases}
x=2+t\cos \alpha, \\
y=1+t\sin \alpha
\end{cases}
\text{(with parameter t)},
$$
where $\alpha \neq \frac{\pi}{2}$. In the polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_{2}$ is $\rho^{2}-6\cos \theta+4=0$.
1. Write the general equation of curve $C_{1}$ and the Cartesian equation of curve $C_{2}$.
2. Given that curve $C_{2}$ intersects with $C_{1}$ at two points, denoted as $A$ and $B$ with corresponding parameters $t_1$ and $t_2$ respectively, when $t_1+t_2=0$, find the value of $|AB|$.

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