
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 following function defined for  integer  $k$ ,

\[f(k)=(k)_3+(2k)_5+(3k)_7-6k\]

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

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