
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 the maximum value of the function $f(x)=A\sin (x+\varphi )(a > 0,0 < \varphi < \pi ),x\in R$ is $1$, and its graph passes through point $M(\frac{\pi }{3},1)$.

(1) Find the analytical expression of $f(x)$;

(2) Find the interval where the function is monotonically increasing.

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