
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 $$f(x)= \begin{cases} 1, & x>0 \\ 0, & x=0 \\ -1, & x<0\end{cases}, \quad g(x)= \begin{cases} 1, & x \text{ is rational} \\ 0, & x \text{ is irrational} \end{cases}$$, then the value of $f(g(\pi))$ is \_\_\_\_\_\_.

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