
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 $f(x)=\begin{cases}1, & x > 0, \\ 0, & x=0, \\ -1, & x < 0,\end{cases}$ and $g(x)=\begin{cases}1, & x \text{ is a rational number}, \\ 0, & x \text{ is an irrational number},\end{cases}$ determine the value of $f(g(\pi))$.

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