
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 $m$ is a specified positive integer, if two integers $a$ and $b$ have the same remainder when divided by $m$, then $a$ and $b$ are said to be congruent modulo $m$, denoted as $a \equiv b \pmod{m}$. For the equation $2^{2010} \equiv r \pmod{7}$, calculate the value of $r$.

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