
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 $f(x) = \ln(x+1)$.
(I) Find the set $A$ of values of $x$ that satisfy $f(1-2x) > f(x)$;
(II) Let set $B = \{x | a-1 < x < 2a^2\}$, if $A \cap B \neq \emptyset$, find the range of the real number $a$.

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