
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 $0 < \theta < \frac{π}{2}$, if $(\sin\theta+\cos\theta)^2+\sqrt{3}\cos2\theta=3$, then $\sin 2\theta =\left(\ \ \right)$.

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