
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 $a > 0$, let $p$ be the statement that the real number $x$ satisfies the inequality $x^{2}-4ax+3a^{2} < 0$, and let $q$ be the statement that the real number $x$ satisfies the inequality $\lg (x-2) < 0$.
(1) If $a=1$, find the range of values for the real number $x$ that make both $p$ and $q$ true.
(2) If $p$ is a necessary but not sufficient condition for $q$, find the range of values for the real number $a$.

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