
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 statement $p: \forall n\in\mathbb{N}^{*},(-1)^{n}\cdot (2a+1) < 2+ \frac{(-1)^{n+1}}{n}$, and the statement $q$: When $|x- \frac{5}{2}| < a(a > 0)$, the inequality $|x^{2}-5| < 4$ always holds.
(1) Determine the truth of statements $p$ and $q$ when $a= \frac{1}{2}$;
(2) If $p\land q$ is a false statement, and $p\lor q$ is a true statement, find the range of values for the real number $a$.

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