
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
A box contains seven cards, each with a function defined on the real number set $R$ written on it. The functions are $f_1(x) = x^3$, $f_2(x) = x^2$, $f_3(x) = x$, $f_4(x) = \cos{x}$, $f_5(x) = \sin{x}$, $f_6(x) = 2 - x$, $f_7(x) = x + 2$. Two cards are drawn at random from the box:
1. How many ways can you draw at least one card with an odd function written on it? (Use a numerical value)
2. How many ways can you draw two cards such that the product of the functions on the cards is an even function? (Use a numerical value)

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