
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
There is a unique function \( f: \mathbb{N} \rightarrow \mathbb{R} \) such that \( f(1) > 0 \) and such that
$$
\sum_{d \mid n} f(d) f\left(\frac{n}{d}\right) = 1
$$
for all \( n \geq 1 \). What is \( f\left(2018^{2019}\right) \)?

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