
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 the parabola $y=x^{2}-2mx-3$ passes through point $A\left(-2,n\right)$, when point $A$ is first moved $3$ units to the right and then moved $b$ units down, it lands exactly on the vertex of the parabola. Determine the value of $b$.

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