
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
Let $\xi$ be a continuous random variable with the probability density function

$$
p(x) = \left\{ \begin{array}{cl}
\lambda e^{-\lambda x}, & x \geqslant 0 \\
0, & x < 0
\end{array} \right.
$$

where $\lambda$ is a positive constant (exponential distribution). Let $\eta = \cos \xi$. Find $\mathrm{P}(\eta < 0)$.

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