
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 a sequence $\{a\_n\}$ that satisfies $a\_1=1$, $|a_{n+1}-a\_n|=p^{n}$, $n∈ℕ^*$.
(I) If $\{a\_n\}$ is an increasing sequence, and $a\_1$, $2a\_2$, $3a\_3$ form an arithmetic sequence, find the value of $p$.
(II) If $p= \frac {1}{2}$, and $\{a_{2n-1}\}$ is an increasing sequence, $\{a_{2n}\}$ is a decreasing sequence, find the general term formula of the sequence $\{a\_n\}$.

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