
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 points $P$ and $Q$ are two points on the curve $y=x^{2}-2x-3$, where the abscissa of point $P$ is $1$ and the abscissa of point $Q$ is $4$, find:<br/>$(1)$ The slope of the secant line $PQ$;<br/>$(2)$ The equation of the tangent line at point $P$.

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