
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 $f(x)=a\sin^3x+b\sqrt[3]{x}\cos^3x+4$ ($a,b \in \mathbb{R}$ and $a,b \neq 0$), $f(\sin 10^\circ) = 5$, find the value of $f(\cos 100^\circ)$.

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