
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
Harry, who is incredibly intellectual, needs to eat carrots  $C_1, C_2, C_3$  and solve *Daily Challenge* problems  $D_1, D_2, D_3$ . However, he insists that carrot  $C_i$  must be eaten only after solving *Daily Challenge* problem  $D_i$ . In how many satisfactory orders can he complete all six actions?

*Proposed by Albert Wang (awang2004)*

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