
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
In the plane rectangular coordinate system $xOy$, the following definitions are given: the greater value of the distances from point $A$ to the $x$-axis and the $y$-axis is called the "long distance" of point $A$. When the "long distance" of point $P$ is equal to the "long distance" of point $Q$, points $P$ and $Q$ are called "equidistant points". If points $P(-1,4)$ and $Q(k+3,4k-3)$ are "equidistant points", then the value of $k$ is ______.

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