
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 the function $f(x)$ defined by 
$$f(x)= \begin{cases} 2x & \text{if } x > 0, \\ f(x+1) & \text{if } x \leq 0, \end{cases}$$
calculate $f\left(\frac{4}{3}\right) + f\left(-\frac{4}{3}\right)$.

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