
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
Let the function $f(x) = \sin(2x + \varphi)$ where $-\pi < \varphi < 0$. The graph of $y=f(x)$ has a line of symmetry which is the line $x= \frac{\pi}{8}$.  
(1) Find the analytic expression of the function $f(x)$.  
(2) To obtain the graph of $y=2\sin\left(2x- \frac{\pi}{6}\right)$, how should the function $f(x)$ be transformed?

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