
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
Determine the true statements among the following propositions:

1. Given $ab \neq 0$, if $a - b = 1$, then $a^{3} - b^{3} - ab - a^{2} - b^{2} = 0$;
2. If the function $f(x) = (x - a)(x + 2)$ is an even function, then the value of the real number $a$ is $-2$;
3. Two points $P$ and $Q$ on the circle $x^{2} + y^{2} - 2x = 0$ are symmetric with respect to the line $kx - y + 2 = 0$, then $k = 2$;
4. If $\tan \theta = 2$, then $\cos 2\theta = -\frac{3}{5}$.

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