
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 first term $a_1 = a$, its sum of the first $n$ terms is $S_n$, and it satisfies the equation $S_n + S_{n-1} = 3n^2$ for $n \geq 2$. If $a_n < a_{n+1}$ holds true for any $n \in \mathbb{N}^*$, find the range of $a$.

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