
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 function $f(x) = \sin 2x - \cos 2x$, consider the following propositions:

1. The smallest positive period of the function $y=f(x)$ is $\pi$.
2. The line $x= \frac{\pi}{4}$ is a symmetry axis of the graph of $y=f(x)$.
3. The point $\left( \frac{\pi}{8},0\right)$ is a symmetry center of the graph of $y=f(x)$.
4. Translating the graph of $y=f(x)$ to the left by $\frac{\pi}{4}$ units results in the graph of $y= \sqrt{2}\sin 2x$.

Identify the true propositions by their numbers.

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