
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 straight line $l$, whose parametric equations are 
$$
\begin{cases}
x = x_{0} + t\cos\theta \\
y = t\sin\theta
\end{cases}
$$
($t$ is the parameter), passes through the left focus $F_1$ of the ellipse $\frac{x^2}{3} + y^2 = 1$ and intersects the positive y-axis at point $C$. It also intersects the ellipse at points $A$ and $B$ (with point $A$ located above point $C$).  
(I) Find the parameter $t_C$ corresponding to point $C$ (expressed in terms of $\theta$);  
(II) If $|F_1B| = |AC|$, find the value of the slope angle $\theta$ of line $l$.

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