
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 maximum value of \\(f(x) = |x-1| - 2|x+1|\\) be \\(m\\).
- (I) Find \\(m\\).
- (II) If \\(a\\), \\(b\\), and \\(c\\) belong to \\((0, +\infty)\\) and \\(a^{2}+2b^{2}+c^{2}=m\\), find the maximum value of \\(ab+bc\\).

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