
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
Given that real numbers \( a \), \( b \), and \( c \) satisfy
\[ 2^a + 4^b = 2^c \]
and
\[ 4^a + 2^b = 4^c, \]
find the minimum value of \( c \).

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