
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 complex numbers $z_{1}=\sin x + \lambda i$ and $z_{2}=(\sin x + \sqrt{3}\cos x) - i$ ($\lambda$, $x \in \mathbb{R}$, $i$ is the imaginary unit).

(1) If $2z_1 = i \cdot z_2$ and $x \in \left(0, \frac{\pi}{2}\right)$, find the values of $x$ and $\lambda$;  
(2) Let the complex numbers $z_1$, $z_2$ correspond to the vectors $\overrightarrow{OZ_{1}}$, $\overrightarrow{OZ_{2}}$ in the complex plane, and $\overrightarrow{OZ_{1}} \perp \overrightarrow{OZ_{2}}$, $\lambda=f(x)$, find the smallest positive period and the intervals of monotonic decrease for $f(x)$.

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