
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 that the function $f(x)$ ($x \in \mathbb{R}$) is an odd function with a period of $4$, and its analytical expression on $[0, 2]$ is:

$$
f(x) =
\begin{cases}
x(1-x) & 0 \leqslant x \leqslant 1 \\
\sin{\pi x} & 1 < x \leqslant 2
\end{cases}
$$

Find the value of $f(\frac{29}{4}) + f(\frac{41}{6})$.

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