
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 Cartesian coordinate system, the coordinates of the center $P$ of a circle are $\left(-3,4\right)$. A circle is drawn in the coordinate plane with radius $r$. When $r$ satisfies ______, the circle $P$ intersects the coordinate axes at $4$ points.

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