
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 function $f(x) = \sin\frac{{πx}}{6}\cos\frac{{πx}}{6}-\sqrt{3}\sin^2\frac{{πx}}{6}+\frac{{\sqrt{3}}}{2}$, where $x\in[-1,a]$, $a\in\mathbb{N}^*$, determine the minimum value of $a$ such that the graph of the function $f(x)$ intersects the line $y=1$ at least twice.

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