
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
Given a positive integer  $k$ , let  $f(k)$  be the sum of the  $k$ -th powers of the primitive roots of  $73$ . For how many positive integers  $k < 2015$  is  $f(k)$  divisible by  $73?$ *Note: A primitive root of  $r$  of a prime  $p$  is an integer  $1 \le r < p$  such that the smallest positive integer  $k$  such that  $r^k \equiv 1 \pmod{p}$  is  $k = p-1$ .*

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