
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 the random variable $\xi \sim N\left(\mu ,1\right)$, and the probability that the function $f\left(x\right)=x^{2}+2x-\xi$ has no zero point is $0.5$. Then $P\left(0 \lt \xi \leqslant 1\right)=$____.<br/>Given: If $\xi \sim N(\mu ,\sigma ^{2})$, then $P\left(\mu -\sigma\ \ \lt \xi \leqslant \mu +\sigma \right)\approx 0.6826$, $P\left(\mu -2\sigma\ \ \lt \xi \leqslant \mu +2\sigma \right)\approx 0.9544$.

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