
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
The number 3600 can be written as \( 2^{a} \times 3^{b} \times 4^{c} \times 5^{d} \), where \( a, b, c \) and \( d \) are all positive integers. It is given that \( a+b+c+d=7 \). What is the value of \( c \)?

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