
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 equations of line $\mathit{l}$ are
$$
\begin{cases}
x= \frac {1}{2}t \\
y= \frac { \sqrt {2}}{2}+ \frac { \sqrt {3}}{2}t
\end{cases}
$$
($t$ is the parameter). If we establish a polar coordinate system with the origin $O$ of the Cartesian coordinate system $xoy$ as the pole and the positive $x$-axis as the polar axis, with the same unit length, we obtain the polar equation of curve $C$ as $\rho=2\cos(\theta-\frac {\pi}{4})$. The line $\mathit{l}$ intersects curve $C$ at points $A$ and $B$. Find $|AB|$.

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