
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 $c > 0$ and $c \neq 1$, let $P$: the function $y = c^{x}$ is monotonically decreasing on $\mathbb{R}$; $Q$: the solution set of the inequality $x + |x - 2c| > 1$ is $\mathbb{R$. Find the range of $c$ if "P or Q" is true, and "P and Q" is false.

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