
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 piecewise function \\(f(x)=\begin{cases} & \lg x, & x > 0 \\ & x+\int_{0}^{a}{3t^{2}dt}, & x\leqslant 0 \end{cases}\\), if \\(f[f(1)]=1\\), determine the constant term in the expansion of \\((4^{x}-2^{-x})^{a+5}\\).

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