
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 $f(x)= \begin{cases} \cos(\pi x), & (x < 1) \\ f(x-1), & (x \geqslant 1) \end{cases}$, find the value of $f(\frac{1}{3})+f(\frac{4}{3})$.

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