
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 "$\sum$" denote the cyclic sum. If \( a, b, \) and \( c \) are given distinct real numbers, then simplify
$$
f(x) = \sum \frac{a^{2}(x-b)(x-c)}{(a-b)(a-c)}.
$$

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