
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 parabola $y=x^{2}-ax-3\ (a\in R)$ intersects the $x$-axis at points $A$ and $B$, and the coordinates of point $C$ are $(0,-3)$. If the circle passing through points $A$, $B$, and $C$ intersects the $y$-axis at another point $D(0,b)$, then $b=$____.

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