
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 number $z= \frac {a^{2}-7a+6}{a+1}+(a^{2}-5a-6)i$ where $a\in \mathbb{R}$.
1. Find the value of the real number $a$ for which $z$ is a real number;
2. Find the value of the real number $a$ for which $z$ is an imaginary number;
3. Find the value of the real number $a$ for which $z$ is a pure imaginary number.

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