
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 proposition $P$: The function $y=\log_{a}(2x+1)$ is monotonically increasing in its domain; proposition $Q$: The inequality $(a-2)x^{2}+2(a-2)x-4 < 0$ is always true for any real number $x$. If proposition $P$ and the negation of $Q$ are true, find the range of the real number $a$.

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