
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
If $f(x)$ is a function defined on $\mathbb{R}$ with a period of $4$, and its expression on $[0,2]$ is given by
$$
f(x)=\begin{cases} 
x(1-x), & 0\leqslant x\leqslant 1, \\
\cos \pi x, & 1 < x\leqslant 2, 
\end{cases}
$$
then find the value of $f\left( f\left( \frac{29}{3} \right) \right)$.

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