
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
Given the function $f(x)=2^{x}- \frac{1}{2^{|x|}}$.
(I) Find the value of $x$ when $f(x)=2$.
(II) Find the range of real number $m$ such that $2^{t}f(2t)+mf(t)\geqslant 0$ holds true for $t\in[1,2]$.

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