
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 range of the function \( f \) defined for integers \( k \) by

\[ 
f(k) = (k)_{3} + (2k)_{5} + (3k)_{7} - 6k 
\]

where \( (k)_{2n+1} \) denotes the multiple of \( 2n+1 \) closest to \( k \).

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