
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
Susan is presented with six boxes  $B_1, \dots, B_6$ , each of which is initially empty, and two identical coins of denomination  $2^k$  for each  $k = 0, \dots, 5$ . Compute the number of ways for Susan to place the coins in the boxes such that each box  $B_k$  contains coins of total value  $2^k$ .

*Proposed by Ankan Bhattacharya*

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