
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 functions $f(x)=\sin x$ and $g(x)=\cos x$, if $\theta$ satisfies that for every $x_{1} \in [0,\frac{\pi}{2}]$, there exists $x_{2} \in [-\frac{\pi}{2},0]$ such that $2f(x_{1})=2g(x_{2}+\theta)+1$ holds, determine the possible values of $\theta$.

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