
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 cosine Fourier transform of the function \( f(x) \), defined in the interval \( (0, \infty) \):

\[ f(x)=\begin{cases} 
0, & 0<x<1 \\
1, & 1<x<2 \\
0, & 2<x 
\end{cases} \]

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