
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
The variable $X$ is normally distributed with parameters $a=2$ and $\sigma=3$. Calculate the following probabilities:
a) $1 \leqslant X \leqslant 2 ;$ 
b) $X \geqslant 2$;
c) $|X-2| \leqslant 3 ;$
d) $X \leqslant -1$;
e) $|X-2| \leqslant 9$.

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