
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
1. Find the value of $$C_{ 3n }^{ 38-n }+ C_{ 21+n }^{ 3n }$$
2. Choose one number from 0, 2 and two numbers from 1, 3, 5 to form a three-digit number with no repeating digits. How many of these numbers are odd?

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