
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
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be an odd function, i.e., a function that satisfies \( -f(x) = f(-x) \) for all \( x \in \mathbb{R} \). Suppose that \( f(x+5) = f(x) \) for all \( x \in \mathbb{R} \) and that \( f(1/3) = 1 \). Determine the value of the sum:

\[ 
f(16/3) + f(29/3) + f(12) + f(-7) 
\]

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