
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
(**4**) Let  $ f(x) \equal{} \sin^6\left(\frac {x}{4}\right) \plus{} \cos^6\left(\frac {x}{4}\right)$  for all real numbers  $ x$ . Determine  $ f^{(2008)}(0)$  (i.e.,  $ f$  differentiated  $ 2008$  times and then evaluated at  $ x \equal{} 0$ ).

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