
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
If two integers $a$ and $b$ have the same remainder when divided by the same integer $m$, then $a$ and $b$ are said to be congruent modulo $m$. That is, when $a$, $b$, $m \in \mathbb{Z}$, if $\frac{a-b}{m} = k$ ($k \in \mathbb{Z}$, $k \neq 0$), then $a$ and $b$ are said to be congruent modulo $m$, denoted as $a = b \ (\text{mod} \ m)$.
(1) If $6 = b \ (\text{mod} \ 2)$ and $0 < b < 6$, then all possible values of $b$ are \_\_\_\_\_\_\_\_\_\_\_\_;
(2) If $a = 10 \ (\text{mod} \ m)$ ($a > 10$, $m > 1$), and the $a$ satisfying the condition are listed in ascending order as $a_1$, $a_2$, ..., $a_n$, ..., when the sum of the first $m-1$ terms of the sequence $\{a_n\}$ is $60(m-1)$, then $m = \_\_\_\_\_\_\_\_\_\_\_\_$.

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