
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
Elective 4-5: Special Topics on Inequalities

Let the function $f(x)=|x-1|-|x+1|$.

(Ⅰ) Solve the inequality $f(x) < |x|-1$;

(Ⅱ) If $m=\frac{3}{4}f{(x)}_{\max }$ and $a^{2}+2c^{2}+3b^{2}=m$, find the maximum value of $ab+2bc$.

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