
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
For the set $E=\{a_1, a_2, \ldots, a_{100}\}$, define a subset $X=\{a_1, a_2, \ldots, a_n\}$, and its "characteristic sequence" as $x_1, x_2, \ldots, x_{100}$, where $x_1=x_{10}=\ldots=x_n=1$. The rest of the items are 0. For example, the "characteristic sequence" of the subset $\{a_2, a_3\}$ is $0, 1, 0, 0, \ldots, 0$  
(1) The sum of the first three items of the "characteristic sequence" of the subset $\{a_1, a_3, a_5\}$ is     ;  
(2) If the "characteristic sequence" $P_1, P_2, \ldots, P_{100}$ of a subset $P$ of $E$ satisfies $p_1=1$, $p_i+p_{i+1}=1$, $1\leq i\leq 99$; and the "characteristic sequence" $q_1, q_2, \ldots, q_{100}$ of a subset $Q$ of $E$ satisfies $q_1=1$, $q_j+q_{j+1}+q_{j+2}=1$, $1\leq j\leq 98$, then the number of elements in $P\cap Q$ is     .

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