
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 complex numbers ${z_1} = 1 - i, {z_2} = 4 + 6i$,

$①$ Find $|{z_1}| + {z_2}$; $②$ If the complex number $z = 1 + bi$ $(b \in \mathbb{R})$ satisfies $z + {z_1}$ being a real number, find $|z|$.

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