
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
Determine the incorrect proposition number among the following statements or calculations:
\\(①6\\) students compete for the championship of \\(3\\) items, and there are \\(3^{6}\\) possible ways to win the championship;
\\(②\\) A school offers \\(3\\) elective courses of type A and \\(4\\) elective courses of type B. If a student chooses \\(3\\) courses and must take at least one course of each type, there are \\(60\\) possible ways to choose;
\\(③\\) For any real number \\(x\\), \\(f(-x)=-f(x)\\), \\(g(-x)=g(x)\\), and \\(x > 0\\), \\(f′(x) < 0\\), \\(g′(x) < 0\\), then \\(x < 0\\), \\(f′(x) > 0\\), \\(g′(x) < 0\\);
\\(④ \\int \_{ a }^{ b }f(x)dx= \\int \_{ a }^{ c }f(x)dx+ \\int \_{ c }^{ b }f(x)dx(a < c < b)\\).

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