
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
Let proposition $p$: Given $c > 0$, $c \neq 1$, the function $y=c^{x}$ is a monotonically decreasing function on $\mathbb{R}$. Proposition $q$: $1-2c < 0$. If $p \lor q$ is true and $p \land q$ is false, find the range of the constant $c$.

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