
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
If $m= \int_{-1}^{1} (6x^{2} + \tan x)dx$, and $(2x + \sqrt{3})^{m} = a_{0} + a_{1}x + a_{2}x^{2} + \ldots + a_{m}x^{m}$, then the value of $(a_{0} + a_{2} + \ldots + a_{m})^{2} - (a_{1} + \ldots + a_{m-1})^{2}$ is __________.

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