
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 $\{a\_n\}$ with the first term $a\_1=a$, the sum of the first $n$ terms is $S\_n$, and it satisfies $S\_n+S_{n-1}=4n^{2}(n\\geqslant 2,n∈N\_+)$, if $a\_n < a_{n+1}$ always holds for any $n∈N\_+$, then the range of $a$ is _______.

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