
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  $n$  be a non-negative integer. Find all non-negative integers  $a$ ,  $b$ ,  $c$ ,  $d$  such that \[a^{2}+b^{2}+c^{2}+d^{2}= 7 \cdot 4^{n}.\]

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