
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
Let the function $f(x)$, where $x, y \in \mathbb{N}^*$, satisfy:
1. For all $a, b \in \mathbb{N}^*$, if $a \neq b$, then $af(a) + bf(b) > af(b) + bf(a)$;
2. For all $n \in \mathbb{N}^*$, $f(f(n)) = 3n$.

Find the value of $f(1) + f(6) + f(28)$.

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