
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 $f(x)=\sin \left( 2x-\dfrac{\pi }{4} \right)$ and $g(x)=\sin 2x$, consider the following statements:

$① f(x)$ has a minimum positive period of $2\pi$;

$②$ The graph of $f(x)$ can be obtained by shifting the graph of $g(x)$ to the left by $\dfrac{\pi}{8}$ units;

$③$ The line $x=-\dfrac{\pi}{8}$ is an axis of symmetry for the graph of $f(x)$.

The correct statement(s) is/are __________.

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