
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 the function $f(x)$ defined on $\mathbb{R}$ satisfy the following conditions simultaneously:
1. $f(x) + f(-x) = 0$;
2. $f(x) = f(x + 2)$;
3. When $0 \leq x < 1$, $f(x) = 2^x - 1$.

Calculate the value of
$$f\left(\frac{1}{2}\right) + f(1) + f\left(\frac{3}{2}\right) + f(2) + f\left(\frac{5}{2}\right).$$

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