
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
If $183a8$ is a multiple of 287, find $a$.

The number of positive factors of $a^{2}$ is $b$, find $b$.

In an urn, there are $c$ balls, $b$ of them are either black or red, $(b+2)$ of them are either red or white, and 12 of them are either black or white. Find $c$.

Given $f(3+x)=f(3-x)$ for all values of $x$, and the equation $f(x)=0$ has exactly $c$ distinct roots, find $d$, the sum of these roots.

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