
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. Solve the following equations in the set of complex numbers:
(1) \(2z - i \bar{z} = 1\);
(2) \(\bar{z} - \lambda z = \omega\) (constants \(\lambda, \omega \in \mathbf{C}\), and \(|\lambda| \neq 1\)).

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