
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 inequality: $\sqrt{x^2 - 3x + 2} > x + 5$

(2) For what value(s) of $k$ does the inequality $\frac{2x^2 + 2kx + k}{4x^2 + 6x + 3} < 1$ hold true for all real numbers?

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