
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
Determine the number of possible increasing arithmetic sequences that can be formed by selecting $m$ terms from the numbers $1, 2, 3, \ldots, n$ (where $m, n \in \mathbb{N}^*$ and $3 \leqslant m \leqslant n$), let this number be denoted as $f(n, m)$. Calculate $f(20, 5)$.

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