
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
On April 23, 2023, which is the 28th "World Book Day," in order to promote the reading concept of "respecting knowledge and advocating civilization," a bookstore held a "Wisdom Challenge Reward Book" activity. The rules of the activity are as follows: There are 3 equally difficult questions, and each challenger has 3 chances. Once a challenger answers a drawn question correctly, they pass the challenge; otherwise, they keep drawing questions until the 3rd attempt. Assuming that Zhang Hua has a probability of 0.7 of answering each question correctly, and whether he can answer the drawn question correctly is independent.<br/>$(1)$ Find the probability of Zhang Hua passing the challenge on the second attempt;<br/>$(2)$ Find the probability of Zhang Hua passing the challenge.

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