
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 that $a > 0$ and $b > 0$ are real numbers, and $a^{2}+3b^{2}=3$, if $\sqrt {5}a+b\leqslant m$ always holds true.

(1) Find the minimum value of $m$;

(2) If $2|x-1|+|x|\geqslant \sqrt {5}a+b$ always holds true for $a > 0$ and $b > 0$, find the range of values for the real number $x$.

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