
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 $\{a\_n\}$ is an increasing geometric sequence, if $a\_2=2$, $a\_4-a\_3=4$,
(I) Find the value of the first term $a\_1$ and the common ratio $q$;
(II) Find the value of the fifth term $a\_5$ and the sum of the first five terms $S\_5$.

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