
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
Suppose $f(x)$ is an odd function defined on $\mathbb{R}$ with a period of $4$. If $f(x)$ is defined as follows on the interval $[-2,0) \cup (0,2]$:

$$
f(x) =
\begin{cases}
ax + b, & \text{if } -2 \leq x < 0, \\
ax - 1, & \text{if } 0 < x \leq 2,
\end{cases}
$$
then find $f(2019)$.

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