
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
A coordinate system and parametric equations problem (4-4):

In the rectangular coordinate system $x0y$, the parametric equations of line $l$ are given by $\begin{cases} x = \frac{1}{2}t \ y = \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2}t \end{cases}$, where $t$ is the parameter. If we establish a polar coordinate system with point $O$ in the rectangular coordinate system $x0y$ as the pole, $0x$ as the polar axis, and the same length unit, the polar equation of curve $C$ is given by $\rho = 2 \cos(\theta - \frac{\pi}{4})$.

(1) Find the slope angle of line $l$.
(2) If line $l$ intersects curve $C$ at points $A$ and $B$, find the length of $AB$.

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