
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
a) In how many ways can a natural number \( n \) be represented as a sum of \( m \) non-negative integers, if the representations \( n = x_{1} + \ldots + x_{m} \) and \( n = y_{1} + \ldots + y_{m} \) are considered identical if and only if \( x_{1} = y_{1}, \ldots, x_{m} = y_{m} \)?

b) Answer the same question for the representation as a sum of natural numbers.

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