
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
Let \( f(x) = x^{2} \) and \( g(x) = 3x - 8 \).
(a) Determine the values of \( f(2) \) and \( g(f(2)) \).
(b) Determine all values of \( x \) such that \( f(g(x)) = g(f(x)) \).
(c) Let \( h(x) = 3x - r \). Determine all values of \( r \) such that \( f(h(2)) = h(f(2)) \).

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