
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 ${f_1(x) = x}$, ${f_2(x) = \sin x}$, ${f_3(x) = \cos x}$, ${f_4(x) = \frac{1}{x}}$, randomly select two functions from these four and multiply them to obtain a new function, determine the probability that the new function is an odd function.

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