
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 $f(x)=\sin \omega x+\cos \left(\omega x+\dfrac{\pi }{6}\right)$, where $x\in R$, $\omega >0$.

(1) When $\omega =1$, find the value of $f\left(\dfrac{\pi }{3}\right)$;

(2) When the smallest positive period of $f(x)$ is $\pi $, find the value of $x$ when $f(x)$ reaches the maximum value in $\left[0,\dfrac{\pi }{4}\right]$.

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