
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 the solution set of the inequality \\(x(x-a-1) < 0\\) (\(a \in \mathbb{R}\)) be \\(M\\), and the solution set of the inequality \\(x^2-2x-3 \leqslant 0\\) be \\(N\\).

\\((1)\\) When \\(a=1\\), find the set \\(M\\);  
\\((2)\\) If \\(M \subseteq N\\), find the range of the real number \\(a\\).

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