
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
In how many ways can the natural number $n$ be written as the sum of two natural addends?

This problem can be interpreted in two different ways. You can either consider the order of the addends as significant or not significant. In other words, you can:

1. Consider that $8 = 3 + 5$ and $8 = 5 + 3$ are the same decomposition.
2. Consider that $8 = 3 + 5$ and $8 = 5 + 3$ are different decompositions.

You are required to solve both tasks.

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