
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
Three statements are given below:
1. The converse of the statement "If $a^2 + b^2 = 0$, then $a$ and $b$ are both 0" is "If $a$ and $b$ are both nonzero, then $a^2 + b^2 \neq 0$".
2. "$m = \frac{1}{2}$" is a necessary but not sufficient condition for the lines $(m + 2)x + 3my + 1 = 0$ and $(m - 2)x + (m + 2)y - 3 = 0$ to be perpendicular.
3. The eccentricity of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 (a > 0, b > 0)$ is $\sqrt{5}$ if one of its asymptotes passes through the point $(1, 2)$.
Identify the number(s) of the true statement(s) among the given statements.

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