
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 vectors $\overrightarrow{a}=(\sin x,1)$ and $\overrightarrow{b}=(1,\cos x)$, where $x\in R$, let $f(x)=\vec{a}\bullet \vec{b}$ .

(1) Find the equation of the axis of symmetry for the function $f(x)$;

(2) If $f\left(\theta+ \dfrac{\pi}{4}\right)= \dfrac{ \sqrt{2}}{3}$, where $\theta\in\left(0, \dfrac{\pi}{2}\right)$, find the value of $f(\theta -\dfrac{\pi }{4})$.

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