
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
A function $f(x)$ defined on $\mathbb{R}$ is odd and satisfies $f(x+4)=f(x)$. Its analytical expression on $[0,2]$ is given by $f(x) = \begin{cases} x(1-x), & 0 \leqslant x \leqslant 1 \\ \sin(\pi x), & 1 < x \leqslant 2 \end{cases}$. Find the value of $f(\frac{29}{4})+f(\frac{41}{6})$.

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