
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
The function \( f(k) \) is a strictly increasing function defined on \( N \) and takes values in \( N \). If for any \( x_1, x_2 \in A \), when \( x_1 < x_2 \), there is \( f(x_1) < f(x_2) \), then \( f(x) \) is called a strictly increasing function on \( A \). The function satisfies the condition \( f(f(k)) = 3k \). Find \( f(1) + f(9) + f(96) \).

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