
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) Given a complex number $z = 3 + ai$ (where $a \in \mathbb{R}$) and $|z| < 4$, find the range of values for the real number $a$.
(2) Let the complex conjugate of $z$ be denoted as $\bar{z}$. Given that $(1 + 2i)\bar{z} = 4 + 3i$, find $z$.

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