
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
Let $n \in \mathbb{N}^*$, $a_n$ be the sum of the coefficients of the expanded form of $(x+4)^n - (x+1)^n$, $c=\frac{3}{4}t-2$, $t \in \mathbb{R}$, and $b_n = \left[\frac{a_1}{5}\right] + \left[\frac{2a_2}{5^2}\right] + ... + \left[\frac{na_n}{5^n}\right]$ (where $[x]$ represents the largest integer not greater than the real number $x$). Find the minimum value of $(n-t)^2 + (b_n + c)^2$.

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