
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
Given \(f(x)=A\sin (\omega x+\phi)\), where \(A > 0\), \(\omega > 0\), and \(|\phi| \leq \frac{\pi}{2}\), \(f(x)\) is an odd function defined on \(\mathbb{R}\), and when \(x=2\), \(f(x)\) reaches its maximum value of \(2\), calculate the value of \(f(1)+f(2)+f(3)+\frac{1}{4}+f(100)\).

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