
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 $f(x)= \sqrt{2}\sin \left( 2x- \frac{\pi}{4} \right)$, where $x\in\mathbb{R}$, if the maximum and minimum values of $f(x)$ in the interval $\left[ \frac{\pi}{8}, \frac{3\pi}{4} \right]$ are $a$ and $b$ respectively, then the value of $a+b$ is ______.

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