
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 $f(x)=x^{2}-1$.

1. For any $1\leqslant x\leqslant 2$, the inequality $4m^{2}|f(x)|+4f(m)\leqslant |f(x-1)|$ always holds. Find the range of values for the real number $m$.
2. For any real number $x\_1\in[1,2]$, there exists a real number $x\_2\in[1,2]$ such that $f(x\_1)=|2f(x\_2)-ax\_2|$ holds. Find the range of values for the real number $a$.

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