
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 a line $l$ passing through the right focus of the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$ intersects the parabola $y^2=4x$ at points $A$ and $B$. If the point $C$ is the symmetric point of $A$ with respect to the $y$-axis, then $\vec{OB} \cdot \vec{OC}=$ \_\_\_\_\_\_\_\_.

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