
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
(1) Determine the intervals of monotonicity for the function $y=\log_{0.7}(x^2-3x+2)$;  
(2) Given $f(x)=8+2x-x^2$, if $g(x)=f(2-x^2)$, determine the intervals of monotonicity and the monotonicity of $g(x)$.

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