
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 that $\omega > 0$, $A > 0$, $a > 0$, $0 < \phi < \pi$, the graph of $y=\sin x$ undergoes the following transformations in sequence: $\text{(1)}$ The vertical coordinate remains unchanged, while the horizontal coordinate becomes $\frac{1}{\omega}$ of its original value; $\text{(2)}$ It moves to the left by $\phi$ units; $\text{(3)}$ It moves upward by $a$ units; $\text{(4)}$ The vertical coordinate becomes $A$ times its original value. As a result, the graph of $y=3\sin (2x-\frac{\pi}{6})+1$ is obtained. Find the value of $A+a+\omega+\phi$.

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