
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 points $A(-3,0)$ and $B(3,0)$, and a moving point $P$ that satisfies $|PA| = 2|PB|$,
$(1)$ If the trajectory of point $P$ is a curve $C$, find the equation of this curve.
$(2)$ If a point $Q$ is on the line $l_1: x + y + 3 = 0$, and a line $l_2$ passes through $Q$ and intersects curve $C$ at only one point $M$, find the minimum value of $|QM|$.

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