
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 $f(x)=3\sin \left( \frac{x}{2}+\frac{\pi}{6} \right)+3$.

$(1)$ Identify the period, amplitude, initial phase, and axis of symmetry for $f(x)$;

$(2)$ Explain how the graph of this function can be obtained from the graph of $y=\sin x$ on the interval $[0,2\pi]$ through transformations.

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