
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
It is known that the function \( f(x) \) is odd, i.e., \( f(-x) = -f(x) \) for each real \( x \). Additionally, it is known that \( f(x+5) = f(x) \) for each \( x \), and that \( f\left( \frac{1}{3} \right) = 2022 \), and \( f\left( \frac{1}{2} \right) = 17 \). What is the value of 

\[ 
f(-7) + f(12) + f\left( \frac{16}{3} \right) + f\left( \frac{9}{2} \right) ?
\]

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