
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]


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A function \( f(x) \) is periodic with period \( T > 0 \) if \( f(x+T)=f(x) \) for all \( x \). The smallest such number \( T \) is called the least period. For example, the functions \( \sin (x) \) and \( \cos (x) \) are periodic with least period \( 2\pi \).

(a) Let a function \( g(x) \) be periodic with the least period \( T=\pi \). Determine the least period of \( g(x / 3) \).

(b) Determine the least period of \( H(x) = \sin (8x) + \cos (4x) \).

(c) Determine the least periods of each of \( G(x) = \sin (\cos (x)) \) and \( F(x) = \cos (\sin (x)) \).

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