
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 general formula of the sequence $\{a_{n}\}$ as ${a_n}=\left\{{\begin{array}{l}{a{n^2}-({\frac{7}{8}a+\frac{{17}}{4}})n+\frac{{17}}{2},n≤2,}\\{{a^n},n＞2}\end{array}}\right.$, if $\{a_{n}\}$ is an increasing sequence, determine the range of real number $a$.

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