
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 that \( f(x) \) is an odd function defined on \([-6,6]\), and \( f(x) \) is a linear function of \( x \) on \([0,3]\), and a quadratic function of \( x \) on \([3,6]\). Given also that for \( 3 \leqslant x \leqslant 6 \), \( f(x) \leqslant f(5)=3 \) and \( f(6)=2 \). Find the analytical expression of the function \( f(x) \).

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