
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
Given that the parametric equation of line $l$ is 
$$
\begin{cases} 
x= \frac{1}{2}t \\ 
y= \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}t 
\end{cases}
$$ 
(where $t$ is the parameter), and taking the origin O of the Cartesian coordinate system $xOy$ as the pole, with the Ox direction as the polar axis, and establishing a polar coordinate system with the same unit length, the polar equation of curve $C$ is obtained as 
$$
\rho = 2\cos\left(\theta - \frac{\pi}{4}\right)
$$
(1) Find the angle of inclination of line $l$.
(2) If line $l$ intersects curve $C$ at points A and B, find $|AB|$.

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