
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
Determine all functionf  $f : \mathbb{R} \mapsto \mathbb{R}$  such that 

\[ f(x+y) = f(x)f(y) - c \sin{x} \sin{y}  \] for all reals  $x,y$  where  $c> 1$  is a given constant.

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