
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
Among the following propositions, the correct one is _______ (write down the correct serial number).

① Given $M(-2,0)$, $N(2,0)$, $|PM| - |PN| = 3$, then the locus of point $P$ is the left branch of a hyperbola;

② Given an ellipse $\frac{x^2}{8-m} + \frac{y^2}{m-2} = 1$ with its major axis on the $y$-axis, if the focal distance is $4$, then the value of the real number $m$ is $7$;

③ The focus of the parabola $y = 2ax^2 (a \neq 0)$ is at the point $\left( \frac{a}{2}, 0 \right)$.

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