
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. In the rectangular coordinate system, the parametric equation of curve C is given by $\begin{cases} x = 2\cos\theta \\ y = \sqrt{3}\sin\theta \end{cases}$ where $\theta$ is the parameter. Establish a polar coordinate system with the coordinate origin as the pole and the positive half of the x-axis as the polar axis. The line $l$ passes through two points $A(\sqrt{2}, \frac{\pi}{4})$ and $B(3, \frac{\pi}{2})$ in the polar coordinate system.

(I) Write the ordinary equation of curve C and find the slope of line $l$.

(II) Suppose line $l$ intersects curve C at points $P$ and $Q$. Find $|BP| \cdot |BQ|$.

B. Given the function $f(x) = |x - 1| + |2x - a|$.

(I) When $a = 1$, find the solution set of $f(x) \geq 1$.

(II) When $x \in [-1, 1]$, $f(x) \geq 1$ always holds true. Find the range of real number values for $a$.

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