
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 $f\left(x\right)=\sin \left(2x+\theta \right)$, where $θ∈(0,\frac{π}{2})$, and $f(\frac{π}{6})=1$.<br/>$(1)$ Find the value of $\theta$;<br/>$(2)$ If $x∈[0,\frac{π}{4}]$, find the range of $f\left(x\right)$.

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