
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 the function $f(x) = a \cdot 2^x + b \cdot 3^x$, where the constants $a$ and $b$ satisfy $ab \neq 0$.
(1) If $ab > 0$, determine the monotonicity of the function $f(x)$;
(2) If $ab < 0$, find the range of values for $x$ such that $f(x + 1) > f(x)$.

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