
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 all functions \( f(x) \) and \( g(x) \) for \( x \in \mathbb{R} \) such that the following equality holds for all \( x, y \in \mathbb{R} \):
\[ \sin x + \cos y \equiv f(x) + f(y) + g(x) - g(y). \]

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