
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 function be \\(f(x) = |2x + 3| + |x - 1|\\).

\\((1)\\) Solve the inequality \\(f(x) > 4\\);

\\((2)\\) If there exists \\(x \in \left[-\frac{3}{2}, 1\right]\\) such that the inequality \\(a + 1 > f(x)\\) holds, find the range of the real number \\(a\\).

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