
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 definition: For \( x \in \mathbf{R} \), if and only if \( n \leqslant x < n+1 \) where \( n \in \mathbf{N}^{*} \), then \([x] = n\). Find the solution set of the inequality \( 4[x]^{2} - 36[x] + 45 \leqslant 0 \).

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