
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
Let \( a, b, c, d \) be odd numbers with \( 0 < a < b < c < d \), and \( ad = bc \), \( a+d = 2^k \), \( b+c = 2^m \), where \( k \) and \( m \) are integers. Find the value of \( a \).

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