
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
During an hour, a switchboard installed to connect telephone devices in a trading firm's offices receives an average of 90 calls. Assuming that the number of calls in any time interval follows a Poisson distribution:

a) Construct the probability distribution series for the random variable \(X\) - the number of calls received by the switchboard within 4 minutes.

b) Find the probability that at least 3 calls will be received within 4 minutes.

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