
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 a function $f(x)$ defined on $\mathbb{R}$ that satisfies $f(x+1) = -f(x)$, and for $x \in (-1, 1]$, the function is defined by 
$$
f(x) = 
\begin{cases}
1 & \text{for } -1 < x \leq 0, \\
-1 & \text{for } 0 < x \leq 1.
\end{cases}
$$

Find the value of $f(3)$.

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