
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
Find the number of functions $f  : \mathbb{R} \to \mathbb{R}$ such that
\[ f(x\sin y) + f(x\sin z) - f(x) f(\sin y \sin z) + \sin(\pi x) \ge 1 \]
for all real numbers $x,$ $y,$ and $z.$

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