
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 $f(x) (x\in R)$ be a periodic function with a period of $4$ and an odd function. The analytical expression of $f(x)$ on $[0,2]$ is given by $f(x)=\begin{cases} & x(x-1), 0\leq x\leq 1, \\ & \sin \pi x, 1 < x\leq 2. \\ \end{cases}$ Find the value of $f(\frac{29}{4}) + f(\frac{41}{6})$ .

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