
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 \\(f(x)\\) is a monotonically decreasing function defined on \\(\mathbb{R}\\), and the real number \\(m\\) satisfies the inequality \\(f(m+1) < f(3-2m)\\). Proposition \\(q\\): When \\(x \in \left[ 0,\frac{\pi}{2} \right]\\), the equation \\(m = -\sin^2 x - 2\sin x + 1\\) has a solution. Find the range of real numbers \\(m\\) for which "proposition \\(p\\) and proposition \\(q\\)" are true.

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